MT5867 Mathematical Logic and Set Theory

Academic year

2024 to 2025 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 11

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

This module is expected to run in alternate even years (e.g. 2022/23, 2024/25, 2026/27, etc.)

Planned timetable

12 noon Mondays (odd weeks), Wednesdays and Fridays

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Prof N Ruskuc

Prof N Ruskuc
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Prof Peter Cameron

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

Mathematical logic is a branch of mathematics which attempts to subject mathematical reasoning itself to a rigorous mathematical treatment, while sets provide a language in which underpins much of contemporary mathematics. In this module we will study both, as well as their interactions. The topics will include predicate calculus, cardinals and ordinals, axiomatic systems for set theory, the beginnings of recursion theory, and the major theorems of mathematical logic, such as compactness and completeness theorems for predicate calculus, as well as Goedel's incompleteness theorem for Peano arithmetic. We will also discuss the ramifications of these results in other parts of mathematics and beyond.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS AT LEAST TWO OF: MT3505, MT4003, MT4004, MT4512, MT4514, MT4515, MT4526

Anti-requisites

YOU CANNOT TAKE THIS MODULE IF YOU TAKE CS3050

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks), 1 tutorial (x 10 weeks)

Intended learning outcomes

  • Demonstrate an understanding of the key concepts in mathematical logic and set theory, such as first order formulas, models, satisfiability, formal proofs, cardinals, ordinals and recursive functions.
  • Produce coherent theoretical arguments (proofs) which establish properties for the above concepts and their relationships with each other.
  • Understand the content and importance of major theorems such as the compactness theorem, completeness theorem, Goedel's Incompleteness Theorem and Zorn's Lemma.
  • Be able to use the above results in analysing specific examples of mathematical theories and in problem-solving.